The Embedding Problem in Galois Theory - Couverture rigide

American Mathematical Society

Couverture rigide

ISBN 10 : 0821845926 ISBN 13 : 9780821845929

Editeur : American Mathematical Society, 1997

Synopsis

The central problem of modern Galois theory involves the inverse problem: given a field $k$ and a group $G$, construct an extension $L/k$ with Galois group $G$. The embedding problem for fields generalizes the inverse problem and consists in finding the conditions under which one can construct a field $L$ normal over $k$, with group $G$, such that $L$ extends a given normal extension $K/k$ with Galois group $G/A$. Moreover, the requirements applied to the object $L$ to be found are usually weakened: it is not necessary for $L$ to be a field, but $L$ must be a Galois algebra over the field $k$, with group $G$.In this setting, the embedding problem is rich in content. But the inverse problem in terms of Galois algebras is poor in content because a Galois algebra providing a solution of the inverse problem always exists and may be easily constructed. The embedding problem is a fruitful approach to the solution of the inverse problem in Galois theory. This book is based on D. K. Faddeev's lectures on embedding theory at St. Petersburg University and contains the main results on the embedding problem. All stages of development are presented in a methodical and unified manner.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 1997
• Langue: anglais
• ISBN 10: 0821845926
• ISBN 13: 9780821845929
• Reliure: Relié
• Nombre de pages: 200
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible